In the present work we concentrate our study on the case where the EoS of neutron star matter is pure hadronic and the hydrostatic equilibrium is described by the general relativistic equations (Tolman–Oppenheimer–Volkoff (TOV) equations) [1]}, [2]}, [3]}, [4]}, [5]}. Moreover, we focus on two possible cases, that the second partner to be a slow rotating neutron star and, in the extreme case, to be a very rapidly rotating one (even close to the Kepler limit). Firstly, we consider that the dense nuclear matter properties are described by the MDI-APR [6]} (MDI: momentum dependent interaction, APR: Akmal, Pandharipande and Ravenhall) nuclear model. This model has recently been applied successfully in similar studies and, according to our opinion, is a robust guide for neutron star studies. However, since the behavior of dense nuclear matter at high densities remains uncertain, the parametrization of the EoS via the speed of sound is almost inevitable, at least in the framework of hadronic EoSs. To be more specific, we construct large number of EoSs where for low densities (concerning the neutron star crust) we employ well established results, but for the EoS concerning the core, we apply a twofold consideration. For the outer part we employ the EoS predicted by the MDI-APR model and for the inner one, a parametrization based on the speed of sound upper limits is applied. In this study, the transition density and the upper limit of the speed of sound are the two free parameters.
